Recent Publications
- ArXiv On Finite Analogs of Schmidt’s Problem and Its Variants, wieh Alexander Berkovich.
- ArXiv Weighted Cylindric Partitions, with Walter Bridges (submitted)
- ArXiv Sequences in Overpartitions, with George E. Andrews (submitted)
- Practical Evaluation of Quantifier Elimination Methods, with James H. Davenport, and Zak P. Tonks. (submitted)
- ArXiv New infinite hierarchies of polynomial identities related to the Capparelli partition theorems, with Alexander Berkovich. J. Math. Anal. Appl. 506 (2022), no. 2, Paper No. 125678, 18 pp.
- ArXiv Reflecting (on) the modulo 9 Kanade-Russell (conjectural) identities, with Wadim Zudilin. Séminaire Lotharingien de Combinatoire, B85e (2021), 17 pp
- ArXiv Cylindric Partitions and some new
Rogers-Ramanujan Identities, with Sylvie Corteel and Jehanne Dousse. (accepted, Proc. Amer. Math. Soc.) https://doi.org/10.1090/proc/15570
- ArXiv qFunctions – A Mathematica package for q-series and partition theory applications, with Jakob Ablinger. Journal of Symbolic Computation 107 (2021), 145-166.
- ArXiv Logconcavity results for a biparametric and an elliptic extension of the q-binomial coefficients, with Michael Schlosser and Koushik Senapati. Int. J. Number Theory 17 (2021), no. 3, 787–804.
- ArXiv Where do the maximum absolute q-series coefficients of
occur?, with Alexander Berkovich. Experimental Mathematics, DOI: 10.1080/10586458.2020.1776177
- ArXiv On a weighted spin of the Lebesgue Identity. Mathematical Aspects of Computer and Information Sciences. MACIS 2019. Lecture Notes in Computer Science, vol 11989. Springer, Cham. https://doi.org/10.1007/978-3-030-43120-4_20
- ArXiv A Polynomial Identity Implying Schur’s Partition Theorem. Proc. Amer. Math. Soc. 148 (2020), 3307-3324
- ArXiv On Double Sum Generating Functions in Connection with Some Classical Partition Theorems. Disc. Math J. Volume 344, Issue 11, (2021), 112562
- ArXiv Refined q-Trinomial Coefficients and Two Infinite Hierarchies of q-Series Identities, with Alexander Berkovich. Algorithmic Combinatorics: Enumerative Combinatorics, Special Functions and Computer Algebra. Texts & Monographs in Symbolic Computation (A Series of the Research Institute for Symbolic Computation, Johannes Kepler University, Linz, Austria). Springer, Cham. https://doi.org/10.1007/978-3-030-44559-1_4
- ArXiv Elementary Polynomial Identities Involving q-Trinomial Coefficients, with Alexander Berkovich. Ann. Comb. 23 (2019), 549–560.
- ArXiv Polynomial Identities Implying Capparelli’s Partition Theorems, with Alexander Berkovich. J. Number Theory 201 (2019), 77-107.
- ArXiv Some Elementary Partition Inequalities and Their Implications, with Alexander Berkovich. Ann. Comb. 23 (2019), 263-284.
- ArXiv Weighted Rogers-Ramanujan Partitions and Dyson Crank. Ramanujan J. 46 (2018), no. 2, 579–591.
- ArXiv On Some Polynomials and Series of Bloch-Polya Type, with Alexander Berkovich. Proc. Amer. Math. Soc. 146 (2018), no. 7, 2827–2838.
- ArXiv New Weighted Partition Theorems with the Emphasis on the Smallest Part of Partitions, with Alexander Berkovich. ALLADI 60 2016: Analytic Number Theory, Modular Forms and q-Hypergeometric Series (2017) pp 69-94 Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 221)
- ArXiv Variation on a theme of Nathan Fine. New weighted partition identities, with Alexander Berkovich. J. Number Theory 176 (2017), 226–248.
- ArXiv On partitions with fixed number of even-indexed and odd-indexed odd parts, with Alexander Berkovich. J. Number Theory 167 (2016), 7–30.
- ArXiv A New Companion to Capparelli’s Identities, with Alexander Berkovich. Adv. in Appl. Math. 71 (2015), 125–137.
Editorial Work
- Guest Editor: Mathematics in Computer Science – ACA 2021 (Virtual Online) Special Issue, with Ilias Kotsireas and Dimitris Simos, published by Birkhauser Springer.
Extended Abstracts
- qFunctions: A Mathematica package for partition theory applications, and its future, Computer Algebra in Scientific Computing 2021 (CASC 21) Proceedings.
- ArXiv The DEWCAD Project: Pushing Back the Doubly Exponential Wall of Cylindrical Algebraic Decomposition, with Russell Bradford, James H. Davenport, Matthew England, and Amirhossein Sadeghimanesh. ISSAC 2021 https://dl.acm.org/doi/abs/10.1145/3511528.3511538
- On q-Rising Factorials and the Necessity of Shared Memory Calculations. Austrian High-Performance-Computing meeting (AHPC2020), Publisher: Institute of Science and Technology Austria, Klosterneuburg Austria, Editors: Alois Schlögl et al. ISBN: 978-3-99078-004-6
Soon to be Public
- On more conjectural identities modulo 16 and 20, joint with George E. Andrews
- Counting on 4-decorated diagrams.